Conventionally, it is known that fuel injection is performed while the engine is stopped in order to cause fuel to be deposited around nozzle holes. Fuel injection that is performed while the engine is stopped is intended to avoid freezing of condensed water and the occurrence of corrosion around the nozzle holes due to deposition of condensed water around the nozzle holes. The proposal to deposit fuel around the nozzle holes is described in Patent Document 1, for example. More specifically, the proposal estimates whether nozzle hole portions at the tip of the fuel injection valve are frozen on the basis of the ambient temperature and the operation time from the engine start to stop, and determines whether fuel should be injected while the engine is stopped on the basis of the estimation result.